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Independent audit: correct QQ16 shear native-frame claim - #2252

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cbethin:codex/qq16-shear-native-frame-audit
Oct 15, 2026
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Mister-Meeseeks merged 1 commit into
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cbethin:codex/qq16-shear-native-frame-audit

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@cbethin

@cbethin cbethin commented Oct 15, 2026

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PR #2216's sixteen-addition shear describes the F0/B1 boundary as a common data frame. The retained interface instead has X_p: F and Y_p: F C_q^-1. This package supplies exact counterexamples to applying its eight Y_T -= X_A updates as bare native scalars on arbitrary payloads. The paired bare updates also fail to conserve the logical selected sum on these inputs.

For a binary character with q dot w = 1, bare subtraction writes -F chi_w; the intended result is -F C_q^-1 chi_w. At target 21 (q=289, w=1), their physical values at address zero are -i and -1. The proof applies to every selected target and every positive tensor length, under the inherited boundary convention. The verifier binds all eight targets to the frozen packet and literal F0/B1 wrappers.

The contribution preserves #2216's reported rank-eight result on payload-constant inputs: all C_q act as identity there. It does not replay that group-algebra calculation. A typed adaptation or fusion with B1 may still implement the logical shear; this audit proves no extra-child lower bound and claims no supplier or new kappa. Its practical purpose is to prevent an unrestricted controller from inheriting the sixteen-addition invoice without a typed implementation.

Validation:

  • Stored Z4 coefficient evaluation checks 4,096 character phases.
  • A separately implemented Gaussian-integer convolution checks eight explicit 512-entry physical vectors, including physical decoding of the nonzero sum change. It imports no predecessor executable.
  • Inverse-line adaptation passes; the positive-line sign and unadapted subtraction fail; constant-payload controls explain the original test's blind spot.
  • Direct optimized replay passes on CPython 3.15.0. The registered package replay passes on its required CPython 3.12.12 environment, an explicit compatibility exception. Metadata, source pins, and git diff --check pass.

One-command reproduction:

python3 -I -O -B research/qq16-shear-native-frame-audit/verify.py

Expected: PASS_QQ16_SHEAR_NATIVE_FRAME_AUDIT rejected_Y_adds=8 same_frame_X_updates=8 character_phases=4096 physical_vectors=8.

The retained core boundary is inherited, not independently re-proved. This is not a full native traversal, hosting, or multiplication-theorem replay. No independent human review or formal-kernel proof is claimed. Base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; audited #2216 head: b80e9ba43367fb8b20877a97da1cb677c34f9264.

Credit Ali Romman and the retained QQ16 lineage for the construction and reviews, and Cinna Davis for the proposed shear. Prepared for Charles Bethin with substantial OpenAI Codex assistance. New material is Apache-2.0. The selected frontier and frozen predecessor files remain unchanged.

@Mister-Meeseeks
Mister-Meeseeks merged commit d91f737 into CrocSwap:main Oct 15, 2026
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Mister-Meeseeks pushed a commit that referenced this pull request Oct 15, 2026
Prices the initial-prefix part of PR #2252's typed-fusion handoff. After
factoring the common completed frame, PR #2216's paired A-to-T shear
followed by B1's eight initial X_T inverse-line normalizations has, for
each selected pair, the endpoint a' = a, t' = C_q^-1 (t + a),
v' = v - C_q^-1 a. At payload characters 0 and 256 every actual q_T has
bit 8 set, so each inverse line changes from 1 to -i; the difference of
the two transfer matrices contains a 16-by-16 minor of determinant
(-1-i)^16 = 256. Free payload-independent scalar gates have zero
character difference and each single-field native line has difference
rank at most one, so rank telescoping gives at least sixteen lines for
any circuit in the model, even with scratch, copies and clears. A typed
one-C0 prefix attains sixteen (eight more than inherited), restoring
every borrowed helper and clearing C0. Fusion with later B1 operations
or cover maps is outside the model; no supplier or kappa change.

Adds research/qq16-shear-prefix-cost/ only.

Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex
research and implementation; packaged with Claude Code).

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
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